हिंदी

Construct the truth table of the following: [(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]

योग
Advertisements

उत्तर

p q r p∧q (p∧q) ∨ r ∼r ∼r ∨ (p∧q) [(p∧q) ∨ r] ∧ [∼r ∨ (p∧q)]
T T T T T F T T
T T F T T T T T
T F T F T F F F
T F F F F T T F
F T T F T F F F
F T F F F T T F
F F T F T F F F
F F F F F T T F
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 6.4 | पृष्ठ ३३

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p


Evaluate: ∫ x . log x dx


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Write the following compound statement symbolically.

The angle is right angle if and only if it is of measure 90°.


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


Construct the truth table of the following:

p → (q → p)


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∧ q) is T


Determine the truth values of p and q in the following case:

(p ∧ q) is F and (p ∧ q) → q is T


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.


Write the truth value of the negation of the following statement.

`sqrt5` is an irrational number.


Write the following statement in symbolic form.

Stock prices are high if and only if stocks are rising.


Find the truth value of the following statement.

Neither 27 is a prime number nor divisible by 4.


If p and q are true and r and s are false, find the truth value of the following compound statement.

p ∧ (q ∧ r)


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ↔ ~(p ∨ q)


If p and q are true and r and s are false, find the truth value of the following compound statement.

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]


If p and q are true and r and s are false, find the truth value of the following compound statement.

~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

Kavita is brilliant and brave.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

The necessary condition for existence of a tangent to the curve of the function is continuity.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If the question paper is not easy then we shall not pass.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

Proof is lengthy and it is not interesting.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r :
Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∨ r


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r


Write the negation of the following.

An angle is a right angle if and only if it is of measure 90°.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


Rewrite the following statement without using the connective ‘If ... then’.

If a quadrilateral is rhombus then it is not a square.


Rewrite the following statement without using the connective ‘If ... then’.

If 10 − 3 = 7 then 10 × 3 ≠ 30.


Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


Negation of “Some men are animal” is ______.


The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______ 


Which of the following is false?


The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______ 


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


From the following set of statements, select two statements which have similar meaning.

  1. If a man is judge, then he is honest.
  2. If a man is not a judge, then he is not honest.
  3. If a man is honest, then he is a judge.
  4. If a man is not honest, then he is not a judge.

Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

  1. Seema is thin and happy.
  2. If Seema is fat then she is unhappy.

Write the negation of p ↔ q.


If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?


Let p: I am brave.
      q: I will climb the Mount Everest.

The symbolic form of a statement,

‘I am neither brave nor I will climb the mount Everest’ is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×